algebraic expressions

9 times a number is that number minus 10 The phrase a number means we define a random/arbitrary variable, let's call it x: x 9 times a number means we multiply x by 9: 9x The phrase that number refers back to the original arbitrary variable we defined above, which is x: x That number minus...

ratio of the squares of t and u Ratio is also known as quotient in algebraic expression problems. The square of t means we raise t to the power of 2: t^2 The square of u means we raise u to the power of 2: u^2 ratio of the squares of t and u means we divide t^2 by u^2: t^2/u^2

There are 7 more jeeps than vans. Define variables Let j be the number of jeeps Let v be the number of vans 7 more jeeps than vans means we add 7 to the number of vans: j = v + 7

kira will spend less than 27 on gifts. so far, she has spent 12$. what are the possible additional amounts she will spend? The key word in this problem is less than. So we know this is an inequality. Let s be Kira's possible spend. We have: s + 12 < 27 To solve for s in this inequality, we...

5 times the product of 2 numbers a and b The product of 2 numbers a and be means we multiply the variables together: ab 5 times the product means we multiply ab by 5: 5ab

You buy 4 magazines for $5 each and 2 drinks for $4 each Calculate total cost: Since cost = price * quantity, we have: Total cost = $5 * 4 magazines + $4 * 2 drinks Total cost = 20 + 8 Total Cost = 28

4 times b increased by 9 minus twice y Take this algebraic expression in parts: Step 1: 4 times b means we multiply the variable b by 4: 4b Step 2: Increased by 9 means we add 9 to 4b: 4b + 9 Step 3: Twice y means we multiply the variable y by 2: 2y Step 4: The phrase minus means we...

x textbooks if one textbook costs $140 Since cost = price * quantity, we have: Total cost = Cost per textbook * number of text books Total cost = 140x

6 times j squared minus twice j squared j squared means we raise the variable j to the power of 2: j^2 6 times j squared means we multiply j^2 by 6: 6j^2 Twice j squared means we multiply j^2 by 2: 2j^2 The word minus means we subtract 2j^2 from 6j^2 6j^2 - 2j^2 So if you must simplify, we...

sum of 5 times h and twice g is equal to 23 Take this algebraic expressions problem in pieces. Step 1: 5 times h: 5h Step 2: Twice g means we multiply g by 2: 2g Step 3: sum of 5 times h and twice g means we add 2g to 5h 5h + 2g Step 4: The phrase is equal to means an equation, so we set 5h...

2 numbers that are equal have a sum of 60 Let's choose 2 arbitrary variables for the 2 numbers x, y Were given 2 equations: x = y <-- Because we have the phrase that are equal x + y = 60 Because x = y in equation (1), we can substitute equation (1) into equation (2) for x: y + y = 60 Add...

add c to d, multiply a by the result, then divide what you have by b Add c to d: d + c Multiply a by the result: a(d + c) then divide what you have by b: a(d + c)/b

2 more than twice the sum of 10 and a number The phrase a number means an arbitrary variable, let's call it x. x The sum of 10 and a number means we add x to 10: 10 + x Twice the sum means we multiply 10 + x by 2: 2(10 + x) 2 more than twice the sum means we add 2 to 2(10 + x): 2(10 + x) + 2

quotient of the sum of 17 and x and y The sum of 17 and x means we add x to 17: 17 + x quotient of the sum of 17 and x and y means we divide 17 + x by y (17 + x)/y

The sum of the sum of x and z and the difference of y and z Take this algebraic expression in 3 parts: Step 1: The sum of x and z is written as: x + z Step 2: The difference of y and z is written as: y - z Step 3: the sum of the sum and difference is written as: x + z + (y - z) x + z + y - z...

If the difference of a number and 4 is multiplied by 3 the result is 19 The phrase a number means an arbitrary variable, let's call it x: x The difference of a number and 4: x - 4 The phrase is multiplied by means we multiply x - 4 by 3: 3(x - 4) The phrase the result is means equals, so we...

g times by 5 then add 3 The phrase times by means times or multiplied by: 5g Then add 3 means we add 3 to 5g: 5g + 3

18 multiplied by the quantity of 11 plus r The quantity of 11 plus r is written as: 11 + r 18 multiplied by the quantity means we take 18 and multiply it by the term 11 + r 18(11 + r)

12 is subtracted from d and the result is tripled. 12 is subtracted from d: d - 12 The result is tripled means we multiply d - 12 by 3 3(d - 12)

3 times the quantity 2 decreased by x is 9 The quantity 2 decreased by x. The phrase decreased by means we subtract: 2 - x 3 times the quantity: 3(2 - x) The word is means equal to, so we set 3(2 - x) equal to 9: 3(2 - x) = 9